parking capacity reduction vs. local code requirements

Yes, you do need to meet the 40% reduction even if code minimum is higher. The intent is that many zoning minimums are higher than they need to be, especially in areas with good transit alternatives. A zoning variance or other special approval can allow the project to go lower. We've taken advantage of transit oriented development zoning incentives on several projects, to avoid building excess parking.  

Hello Emily,  Thanks so much for your answer. Could a solution be locating some of the parking underneath the building (or under a green canopy)?

This credit is more about reducing the number of parking spaces than reducing the open area dedicated to parking (see Open Space, Heat Island, and Rainwater Management for that). So you really just need to get the total number down to the LEED required level. Some strategies I know of for negotiating a lower number with the local agency would be sharing parking with other buildings, reducing parking because you are developing near transit, or developing a policy to support commuters who don't drive with carpooling, guaranteed ride home, shuttles to transit, etc.